Sobolev functions on infinite-dimensional domains

Abstract

We study extensions of Sobolev and BV functions on infinite-dimensional domains. Along with some positive results we present a negative solution of the long-standing problem of existence of Sobolev extensions of functions in Gaussian Sobolev spaces from a convex domain to the whole space.

28 pages

References in corpus (1)

• Dirichlet spaces on H-convex sets in Wiener space